Decryption Exponent

Synonyms

Private exponent

Related Concepts

RSA Digital Signature Scheme; RSA Public-Key Encryption

Definition

The exponent d in an RSA private key (n,  d) is called the decryption exponent. It is related to the encryption exponent e by the relation that the product by the relation that for all messages m, ${({m}^{e})}^{d} \equiv m\ mod\ n$. This relation is satisfied if the product $\rm{e} \cdot \rm{d}$ is congruent to 1 modulo $\phi (n)$, where $\phi (n)$ is > Euler’s totient function. (It is also satisfied if $\rm{e} \cdot \rm{d} \equiv 1\ mod$ λ(n), where λ(n) is a certain function of the prime factors of n that divides ϕ(n), although the ϕ(n) relation is more commonly used.)

Decryption of a ciphertext c works by raising c to the power d modulo n.